Question

An automobile manufacturer claims that its van has a 39.0 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 120 vans, they found a mean MPG of 38.8. Assume the standard deviation is known to be 2.2. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.

Answer 1

Answer: z=-1.00

Step-by-step explanation:

Given : Population mean : $\mu=39.0$

Sample size : n=120  ;

Sample mean: $\overline{x}=38.8$  ;

Standard deviation: $s=2.2$

Test statistic for population mean:

$z=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}\\\\\Rigtarrow\ z=\dfrac{38.8-39.0}{\dfrac{2.2}{\sqrt{120}}}\\\\\Rightarrow\ z=-0.995859195464\aprox-1.00\ \ \text{[Rounded to 2 decimal places]}$

Hence, the value of the test statistic : z=-1.00